[School of Natural Sciences PhD Scholarships] Dynamic, individualised prediction of the kidney–heart cascade: multistate joint models for irregular primary care and hospital data

About the project

About the Project Kidney disease and heart disease feed each other. Kidney function declines, cardiovascular risk rises, and a cardiovascular event or its treatment damages the kidneys further. The risk scores used in practice do not follow that loop: they are calculated once, from one blood test, and never updated. This PhD builds the statistics to do better. You will develop multistate joint models in which repeated kidney and cardiovascular measurements drive movement between disease states in both directions, using anonymised records for millions of patients in the Clinical Practice Research Datalink linked to hospital and mortality data. The methodological problems are real ones. The biomarker that predicts an event is itself changed by that event, so the usual joint model with a single terminal endpoint does not apply. Routine measurements are not taken at random: sicker patients are tested more often, and the visit process and the disease process share the same unobserved health state, which puts identifiability of the association in question rather than taking it for granted. Kidney function is inferred from a single blood result and staged under a confirmation rule, so the driver of every transition carries non-classical measurement error. Fitting such a model to millions of records requires approximate Bayesian inference, and whether the approximation keeps predictions calibrated is part of the research. The result is a risk prediction that updates itself: each new test result revises a patient’s predicted risk with honest uncertainty attached, and you will establish how much measurement history a patient needs before their own prediction can be trusted — a question current risk tools never ask. Models are validated across practices, regions and time periods and compared with the equations in use today. Training covers Bayesian computation at scale, survival and longitudinal modelling, the curation of linked electronic health records, and the communication of uncertainty to non-technical audiences. Supervision is shared between the Department of Mathematics at Manchester, which leads the statistical and mathematical core, and the Division of Population Health and Genomics at Dundee, which leads joint and multistate modelling, dynamic prediction and work with licensed routine health data. The project is part of an established collaboration between the two universities. You will have access to high-performance computing, licensed national health data, doctoral training courses, active seminar programmes in both groups, and funded travel to present annually at a national meeting. You will finish with published methodological work and the ability to move between statistical theory and national health data science. The project suits a mathematically strong candidate; no clinical background is needed. This project is expected to start in September 2027. Before you apply: We strongly recommend that you contact the supervisors for this project before you apply. How to apply: To be considered for this project you must complete a formal application through our online application portal. If you already have an applicant account this link will directly open an application for PhD School of Natural Sciences Scholarships . If you don’t already have an applicant account, please follow the instructions here . When applying, please specify the full title and supervisor/s of the project, details of your previous study, and names and contact details of two referees. You must also upload a Supporting Statement describing your motivation to apply to the project, your CV and transcripts of awarded and in-progress university qualifications . Please note late or incomplete applications will not be considered. Equality, diversity and inclusion are fundamental to the success of The University of Manchester and central to all our activities. A diverse research community strengthens creativity, productivity and quality, while increasing the societal and economic impact of our work. We welcome applicants from all career paths, backgrounds and sections of the community, regardless of age, disability, ethnicity, gender, gender expression, sexual orientation or transgender status. We welcome applications from candidates returning to study after a career break or experience in other roles. Flexible study arrangements may be available, including part-time study at 50%, 60% or 80%, subject to the requirements of the project and funder. Eligibility : The standard academic entry requirement for this PhD is an upper second-class (2:1) honours degree in a discipline directly relevant to the PhD (or international equivalent) OR any upper-second class (2:1) honours degree and a Master’s degree at merit in a discipline directly relevant to the PhD (or international equivalent). Previous research experience or Degrees in Statistics, Mathematics, or allied areas (with a substantial background in statistics). Skill in R programming (substantiated by curriculum taken and/or projects). Proficiency in oral & written communication in English, and an interest / research experience in (statistical) modelling and analysis of spatio-temporal data is desirable. This project will remain open until filled. If your application is submitted by 1 st November 2026, you can expect a decision by 18 th December 2026. If your application is submitted by 15 th January 2027, you can expect a decision by 30 th March 2027. Self or externally funded students can also be considered for this project. FSESoNS

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